Marital Issues - Advice??

Amanda
This is super long, so brace yourselves!
So here's a little background information for you:
My husband and I have been best friends since we were 10 years old (we are now 21). We've been together 4.5 years and married for 2. We started dating our Junior year of high school, we're together just over a year when I got pregnant with our first daughter. We went though a rough patch during the time I was pregnant, but stayed together. 
I started college and my daughter was born after my first semester at ASU. After she was born, he asked me to marry him when she was 2 months old, and 4 months later we got married in a little church in our hometown. It was magical and the most special day of our lives! We were so in love and both cried hysterically during the ceremony when we made eye contact while I was walking down the isle. 
2 weeks after our wedding, someone messaged me on Facebook telling me that my husband had cheated on me when I was pregnant. My husband came clean and it had been true. He had been having sex with one of his friends for 4 months during my pregnancy, but he had ended things a while back, and he realized what he wanted and that's why he asked me to marry him. I have always loved him and we had a child together, so I decided to stay true to my wedding vows of for better or worse, and I decided to forgive him  and we fixed our relationship. 
About a year later, I got pregnant with our second daughter (we had been trying, and both wanted another baby). We were both thrilled to be bringing another little human into our lives and my husband was very helpful to me and loving during my second pregnancy. He even let me quit my job so I could rest and stay home with the kids while I finished up my classes at ASU, and so I could remain focused on my studies, as I was planning on graduating with my bachelors a year early. 
When my youngest daughter was born, he got weird. Not a scetchy weird, but almost a postpartum depression for men.. I have been breastfeeding (my daughter is 7 months old now) and he hasn't had much chance to bond with her, as he got promoted a few months ago to a GM of a restaurant and works 60 hours a week and is never the one to feed her or take care of her, since only I get up with her at night because there's no since in both of us getting up if she just wants to be fed. He adores our oldest, but he has told me several times before how he loves our youngest, but doesn't like her because she cries a lot and is pretty high maintenance. It has been upsetting me, because I really wanted this baby (and he did too - or so I thought). 
Just last week, I graduated from ASU. We were living in family housing on campus before, and had to move a few weeks ago due to my graduation. All of us are so in love with our new home and have been so happy. My husband and I have been having sex like bunnies! Since he works a lot, I have been in charge of gathering the last few things from our old house, and unpacking the new one. I also have been applying to jobs and haven't heard anything back yet. 
Last night, we got into an argument about dinner *i know, so ridiculous right?* and of course it turned into a bigger argument about all the things that each of us do wrong. I explained to him how it bothers me that he doesn't care for our daughter, and that I wished he would appreciate the things I do around the house because being a stay at home mom is hard, and unpacking by myself has taken a toll on my energy level. 
He got upset, and told me that he works for 12-16 hours a day and comes home and nothing is done. He also wants me to get into more of his hobbies, and He also says that I need to get a job and then I will understand what it's like to work so hard. I get that he is tired from work, and I know I could do more around the house (but I like my breaks when the kids finally take a nap). 
There is also so much that I do around here that goes unnoticed. For example, doctors appointments (for me and both of my daughters), I make sure all of our bills are paid on time each month, I deal with facilities and utilities people when something isn't working properly, I get the mail, I do the grocery shopping, I serve my oldest child 3 meals a day not including snacks, and my youngest eats every 2-3 hours. I feed and take out our dog, I take out trash, I change at the very least 10 diapers a day, I bathe our kids, get them dressed and I cut my oldest child's hair 2x a month, I do laundry, and up until recently I had 6 classes to do homework for. He gets mad because sometimes dishes pile up and I have a hard time finding the time to deep clean the house. (It's not very messy anyways, we are both pretty clean and I've taught my daughter to pick up after herself. And I always clean dishes, even if I don't get to them for a few days). 
I get why he is upset. He wants to physically see something being done, so he knows that I am not sitting around. But his attitude towards me makes me not want to do anything at all. 
But here's what I did that was stupid. 
He has a new friend that he met through work recently. He has a truck and he helped her move because her husband left her and her baby high and dry without a word. He means well, and has good intentions but I am a crazy psychopath because of what he did before and I occasionally look through his phone. This morning, everything was tense, but fine and I decided to be nosey and look through his phone while he was in the shower. I noticed that he had deleted his messages from this girl last night after our argument, so I confronted him and told him that I trusted him, but I wouldn't continue to do so if he kept giving me reasons not to. 
He blew up at me (because I do this every once in a while - I am possessive of him and act like this every time there is a female friend) and told me that I need to stop acting like this and that he obviously loves me because we've been together so long and have two kids. He also showed me a picture of her.. and she is super not his type. Just saying. I still don't know what they had been talking about. 
Anyways, I know we are both in the wrong, and I definitely feel like an asshole. But the question is, how to we go about fixing the things that make each other upset? We have had these arguments more than a couple times, and I just want them to go away. We're both in love and want to be together but we both feel this same argument is getting old!