I get a few hours after they're in bed and before I go to bed in which to cram cleanup, catching up with my wife, and other bits of essential life maintenance.
It does get easier as they age. Our youngest is three, so I have a while before the "hanging off my legs" phase is done, but I can remember the era of newborns, when I could be interrupted at any moment, and I couldn't count on an entire hour to myself at any point during the day or night.
(FWIW, a big part of making this work is shifting your mindset to appreciate the little things and recognize how precious they actually are. At this point I cherish being woken up by a wailing toddler and rocking her back to sleep, because I know I won't get many more moments in my life when she's a tiny little bundle snuggled up and cozy against my chest, and it's truly magical when I manage not to be hung up on anger over being woken up at 3 AM.)