Husbands depression

My husband suffers depression which he fairly recently acknowledged and has since been on medication. The medication is helping a lot but recently I feel he is slipping back again and I'm not really sure what to do. Most of the time he comes across fine but then he has days where he is very lazy, moody and can be quite immature (he's 35). He also struggles with social anxiety as well.
I have caught him out a few times in recent years saying inappropriate things via fb groups he's in and messenger to women, alot was while I was pregnant with our lady baby. When I question him he says it's all just for a laugh and I'm too much of a prune.
I recently found messages on his fb where the chat starts off between him and a girl he used to go to school with, with both of them saying things like 'hey spunky' and 'Good morning hot stuff!'. I found the same type of things with the same person before and he deleted them before he thought I'd seen them. It then goes on to be innocent chatting but am I wrong for being hurt by this?? She lives on the other side of the country now so I know nothing would ever happen but I still feel hurt. He has also become sex obsessed! We have 3 kids, one who is only 3 months old. That along with a lot of sickness in our house lately means we haven't had much sex. I explain to him why I don't feel like it and still try and be affectionate but he takes it really personally and gets quite depressed. When I talk he's always more prooccupied with his phone or PlayStation to really listen.
I have also found today that he is in a group for anxiety and depression on fb, and has been sharing a lot of quotes about feeling alone and nobody understand how he feels. I'm doing my absolute best to get him to open up but he just brushes it off and tells me he's fine. We are normally so happy and I love him and our family so much but I just feel like he won't let me in anymore :(