he's not understanding, in need of advice...

So my current job is very stressful on me, my department has a supervisor, she's the boss, but I'm like "the second supervisor" with just a normal title like everyone else in the department besides her. for example I run her shifts on her days off, do all of the same things she does (placing orders, opening shift, perishables, signing papers, etc.). I am the only other person in our understaffed department who is trained to do her job when she's not there. I am also one of 3 people including her that have been with the department since the day it opened. Not only am I trained in my department but I'm also trained in some areas of the department we branch off from and when the manager needs something done he comes to me to do it, including training people on how to do things and doing them myself. Today for example I worked the supervisor shift while performing my own duties as a regular employee and trained a new employee and a current one in our department, taught a MOD an aspect of our department, and worked my 8 hour shift plus an extra 50 min with no lunch break. Had a person who just started 2 weeks ago call off and quit and had the other worker leave for an anxiety attack, helped the MOD find coverage, made sure everything was in order before I left and will be going in an hour early to work on things that couldn't get done today. I know my department couldn't manage without me but yet they are still not meeting my needs (fulltime, benefits, raise) and seeing that our department is a 12 person department and we only have 5 people including me I don't see how that could be an issue but apparently it is. So now it comes down to where my SO isn't understanding my want to stay because I would feel guilty leaving and the fact that I have an interview with a company coming up that will offer me more money, full time, and benefits after 90 days, and he wants me to take that opportunity should they offer me a job with no consideration for my current job. he also has an issue with the fact that I decides looking for a new job but now want to stay after I told him I was training a new guy today. But they have no coincidence.Im just not sure what to do. if it wasn't for the shitty management on the higher end I wouldn't consider leaving. I just need some advice. willing to answer any questions should anyone need further detail.