I had an elcs, which should have all gone to plan as far as dp was concerned, but went a little bit pear shaped.
I had my pre-med and dp was told that he couldn't be in the room while I had the epidural, but they would come and get him as soon as I had had it. Unfortunately, there was an emergency and I was kept waiting for half an hour or so. But nobody told dp, so he was worried and panicking that something had gone horribly wrong.
When they did let him in, though, they did the op, and asked if he wanted to go to the other side of the screen to see ds being born (he didn't) They handed ds straight to dp and left him to bathe him and dress him whilst they stithced me up.
It was a lovely time for dp, as I wasn't even there, so he got to spend some really nice time on his own with ds.
Obviously, as it is your bf's dp's first, they may not give the baby straight to him, and he may feel uncomfortable dressing and bathing the baby, etc, but it's something for them to think about.
Dp did feel that after that he was ignored again, though - I was in the hospital and he was a "visitor" rather than a part of what ds and I were (iykwim)