My husband works full time too. When our daughter was born I used to go to bed at around 7pm after I fed her and he'd bring her up at around 10pm for another feed then either put her in bed or stay up with her until around midnight depending on how sleepy she was. He'd then get up with her at around 5:30-6 and give me an hour in the morning too. We eventually ended up switching the 10pm feed for formula so I got a really good stretch of sleep.
I didn't want him to wake up during the middle of the night, it was my own personal preference as I breastfed through the night and I didn't see the point in us both having disrupted nights but he was willing to get up had I made the decision that I wanted him to.
We're now due our second imminently and we've already agreed we'll follow a similar structure again - I'll go to bed when my toddler does at around 8pm, he'll bring baby up at around 10/11 then I'll do the night feed and he'll get up with the baby anytime from 5am. Then our toddler will join us in bed whenever she wakes up while he gets ready for wok and she gets ready for nursery.
This baby isn't just yours, they are your husbands too and he also has to take 50% responsibility. He can't just live like sleeping beauty because "he works full time". Looking after a baby is demanding and relentless and you'll end up in a really bad place if he doesn't start pulling his finger out.
I also couldn't nap during the day, I was too switched on and on edge and my baby would not let me put her down, she lived for contact naps.
However, it did get much, much easier and it all seems so long ago now. That doesn't mean that you should settle for a husband and dad that doesn't pull his weight.