Well, in our case (both working FT and up to recently both commuting up to an hour, but DH now working 10 mins from home) - one does mornings and the other does evenings. So I get up, get MYself ready, and go, in the mornings. DH gets DD up, organizes breakfast and school lunch, admittedly hands over to a minder for the hour before DD needs to be in school, but does the morning stuff before he leaves (minder was necessary before his commute changed, and it is worth it to keep her on for a few reasons).
I finish up earlier than DH, get home to collect DD from afterschool club and make dinner (admittedly, it may be made and cooking in oven, or half prepped from yesterday - but I get it organized and on the table). DH gets home about the time dinner is ready, or may work later and eat when he gets in.
We tend to share the housework. I tend to be the planner and organizer in advance, and do the shopping (although that is often organize the internet delivery).
It works for us. We alternate if one has a meeting or other commitment at the "wrong" end of the day for us - just let each other know in advance. And occasionally one or other needs to do the 2 ends of a day for various reasons, but it balances out over time.
If your DH is at home, can he prep dinner while taking his lunch break? Can he be in to supervise grocery delivery? If his afternoons are busy, could he take total control in the mornings and let you go for your commute?