In a very similar situation here, but it is both of us who don't like condoms not just dh, but being off the oral contraception I am a completely different person.
Having come off the pill and decided to see about getting a copper coil I contacted the local sexual health clinic to sort out an appointment. Can't get first appt for 4 weeks, then a minimum of another 4 weeks for fitting, so decided to bear with the pill for the next couple of months, knowing I'd be coming off it soon will help me get through it.
So went to the gp for a discussion about the whole thing and get a short supply of POP. She was great and confirmed she thinks I am doing the right thing getting off the hormones, especially as I have had depression and the pill affects that too. Mirena/hormone coil contains hormones so will likely have the same side effects as oral contraception, so she wouldn't recommend that, same with depo and implant, so no go there. Only other real option as far as dh, gp and I can come up with is the copper coil. We have considered sterilisation as have dc anyway but not completely comfortable with either option there. We have tried condoms every so often in the past and both hate them, so had discounted them.
As an aside, we are church goers and yesterday asked someone at church for prayer help to get through the next few weeks. In the conversation that ensued they asked about condoms and I said we both hated them. They suggested experimenting with different kinds as we might find a suitable one, so I could come off the pill for the next few weeks. So now we have the thin ones and the skin feel ones. Tried the skin feel last night, no sensation for either dh or me. Will try the thin ones but not too hopeful now, so I can understand your partner disliking them, but don't know what reason he has for that. But, have you tried different ones with him? There might be a particular 'patterned' one that works, or a different size? Or have you tried them all? (Sorry if tmi!)
There is also the diaphragm or cap to consider, but they have lower success rates. We have also discounted them for more than one reason, but might be worth considering them for you? Or the femidom, but I know nothing about it.
Our only option is copper coil or not having sex at the moment, so I'm going to try the coil. When not on the pill there is no chance I will be able to abstain, so need something. When on the pill my libido became so low we did not need it as didn't dtd for 6 months, became a joke that the pill did its job in more ways than one.
Sorry I can't tell you about my experience with the copper coil yet, not having got mine yet. There will be others who can help with that, I am sure.