I think there are two different kinds of jealous when it is between a hubby and the stay at home mom.
The first type: the Hubby sees how much more time the mom gets to spend with the child(ren) and wishes he can be there enjoying all those fun moments... my hubby had this type of jelaousy, we also noticed we kind of "sat" around or did house work at home on the weekend while my daughter and I did the "fun things" while hubby was at work. So we always do one family fun thing on the weekend unless we have declared it a no event weekend, that way hubby is part of some happy fun memories. This has helped my hubby, he was always coming home and having to be the enforcer because I was pushed to my limits by the time he got home... have a fun thing planned on the weekend let him be a fun dad, I have also encouraged him to read & play a game with my daughter every day while I cook dinner that way he has an activity besides enforcing rules during the week.
The second type: the Hubby thinks we have the easy job (or no a job at all) and we get to sit around at home and do nothing all day. As we all know stay at home mom cleans, cooks, does laundry, takes the child(ren) places, errands and so on which really is a job and takes up a lot of time. The Hubby may not realize all that you do and that you work as hard as he does it is just a different type of job. If he says he thinks you have the easy job then tell him all you do and have him take care of the kids for a few days so he can see that is a big job and you do not just sit around.
Have you asked him why he really is jealous? I know you said he is jealous because you stay home with the kids but why, that will help pin point the issue. Have to get to the root of the issue, ex: he thinks you just laze around at home and he wants to do that instead of you, he wishes he was home with the kids because he is missing out on all the fun... in the end this will be an issue he will have to work on, there is not a whole lot you can do to help unless hubby becomes at ease with it first.