My mum won't even wear a non padded bra after my dad gave her years of these sorts of comments about her nipples being "on display", that blokes would stare, that people would think she was "up for it", that she was dressing "inappropriately", etc.
I've no clue how she raised 3 girls to not be ashamed of their nipples
but we came out of it unscathed and often try and point out to her that EVERYONE has nipples. "Oh well your dad made me feel self conscious" (and this was with a bra on, but not a padded one). "Oh I HAVE to have a padded bra, so you know, my nipples don't show." As if they're something dirty and shameful. 
My dad had issue with this like your DP. My dad is a controlling, abusive, sexist, arsehole that none of us have anything to do with. My mum hasn't lived with my dad for about 25 years and she still lives with this self consciousness about showing her fucking nipples, it makes me furious.
My advice is wear what you want, ignore him and seriously consider if you want to end up like my mum, with no self esteem and ashamed of having breasts and nipples. 
I'm rather large in the boob department so prefer to have a bra on, but when I take it off for bed my DP doesn't comment either way, other than an acceptable compliment e.g. "nice boobs".