It's not "flu" but sounds like a stomach virus your kids shared and your husband may have too. Foodborne illnesses usually would not pass among the kids like this unless they all ate the same contaminated food item, or were exposed to each others' vomit or feces (secondary exposure). If it was foodborne, it could be over with pretty quickly but that depends completely on what pathogen it was -- and you won't know unless your kids were/are sick enough to warrant getting them tested, which thankfully does not seem to be the case.
(If your baby continues to be lethargic, though, get him to a doctor tomorrow; younger kids can be much more affected by either viruses or foodborne illnesses than older kids.)
I would bet it's a fast-acting virus. Stomach viruses are virulent and spread rapidly and easily, especially where there are young kids and lots of vomit to clean up. If your husband even seems sick with this, even if he's not vomiting yet, isolate him to one bathroom the kids do not use and ensure that he keeps his hands extremely clean; wipe down all the doorknobs often (a really classic place for viruses to get spread is on doorknobs and other areas people touch and then kids touch after them), etc. Next time see if you can isolate the vomiting kid for a whole day so no one uses the same bathroom as the one who is ill. Isolation, if you can do it, is a huge help.
If any of the kids start vomiting again after seeming to recover -- get them to a doctor ASAP. If you have ANY suspicions that food in the house caused it, keep some to have it tested and keep packaging, but it sounds like a virus. Don't hesitate to ask your pediatrician's office (they do have a phone number for questions 24/7, I hope!) what they think.