I presume, as your DH has now gone to gym and work, that on his return tonight, he will be handed the 3 DCs and responsibility for making dinner for the whole family, and getting the rest of the laundry sorted, while you get a sleep?
Like a previous poster, in our house, we both work but DH is as if not more hands on at night. He often hears DD faster than me (he is insomniac whereas, if properly asleep, I sleep deeply and don't hear her) and is up and dealing with her if he can. If it's a "normal" issue (nightmare, hungry, bathroom) he often deals with it. If she is getting sick, he will usually be well into dealing with it (I usually do wake up with the noise of that) and we tag team getting her sorted - finish getting sick, then getting cleaned up and warm, and comfortable again back in bed. Usually involving cleaning carpets (she has a basin but often forgets about it) as well as changing her bed. And throwing a load into the machine to run either straight away or later when we will be up again. If it's a follow-on incidence (not uncommon), the first load of washing is thrown onto clothes horse if middle of the night or tumble dryer if late enough to be almost getting up time and second lot into washer.
And when she was a baby, and bugs meant keeping her out of crèche, we would tag team that as well - he was able to get into his building early in the mornings (mine not open until 7am) and would get a good start while I looked after her. I'd come in and meet him at lunchtime, to do a handover by car if she was well enough (at home if not), and he'd bring her home while I worked a long afternoon (my building stays open until 8pm) and we'd both do more later at home, so we'd get most of a day's work done still. And we'd juggle who had meetings around that general "norm" of emergencies pattern, moving them and making sure we each got to the important ones.
Learn to wake him earlier - and share the jobs in the middle of the night.