Husband reluctant to watch kid alone

Kw

Hey first time parents here. We have a 5month old daughter and my husband won’t watch her alone if I leave the house more than 30min. And even when I am home he doesn’t change diapers or do anything to “take care of her”. I bathe her, change diapers, feed her, put her to bed, and am usually the one playing with her. He will watch her when I shower or if I cook or something. But if during the day I ask if he wants to hold her he will say “can you put her in the bouncer?” Again, he does hold her and talk with her and try to make her laugh, but not as often as expected.

I understand the feeding because she is breastfed, though she does take a bottle easily. But wish he would help with baths or diapers occasionally, but really wish he would feel comfortable watching her alone. He usually says “sorry I don’t have a boob to just whip out and feed her if she gets fussy” I then remind him we have perfectly good bottles available.

He is a great husband because he works 6:30am-3:30 during week, and will work on our house on evenings and weekends. He also does dishes and cleans probably more than I do.

Obviously I appreciate him doing those things but wish I could go to grocery store or somewhere and be able to leave her with him.

Am I being ungrateful for him doing a lot of housework but not helping much with care of kid? Or am I right in my feelings? Any tips on how to discuss it with him?