Kids do adjust, but I would suggest some kind of counseling. Some schools have counseling or groups for kids that have separated or divorced parents (our school had one called the banana splits). My middle daughter was already going for therapy for other reasons, so I had us all go to talk about it.
Talking to a counselor or someone other than family can help, they can vent out their feelings and validate them without worrying about hurting you or your husbands feelings. They might not say anything to you but say it to others.
My kids have adjusted pretty good, i think it is because they were used to their dad not being there for them. I had two things happen that were a bit unsettling. My youngest who was around 8 at the time, had a friend whose parents had separated for a year and got back together.. well this little girl told my daughter to write us notes saying we should be back together because "it worked" for her. That was difficult, but she is better now. The second incident was when me and the kids moved out. All three of my girls (including my oldest who just turned 19) felt uncomfortable going back to the house with their dad living there with roommates. They said that being there without me was hard. Its always going to be difficult, but if you and your husband are civil to each other and the kids see that you both love them, they will be ok. good luck!