THE BIG DEBATE: Is It Possible To Maintain A Casual Relationship With An Ex-Lover?

Not everyone is fortunate enough to get married to his/her first love. For some of us, we go through several exes before finding our right life partners.  At some point, others even may think they have found the right partner, get married, and later find themselves divorced.  For some of us, we run through a few hurdles before settling down with our Adam or Eve.
Some of my relationships have ended not because I had a fight or any bitter encounter with my exes.  One of my relationships ended because my partner was not ready for marriage.  Another ended because I traveled out of the country.
In instances like these, I tend to keep a friendship with the ex.  I trust myself enough to know that it is over, and that nothing sexual can ever happen between us as friends.  With that idea in mind, I have been able to maintained friendship with my exes for years, but down the line I met my current husband.
He is a great guy and loves me to death, but he doesn’t believe that I should continue to keep such relationships.  I questioned his trust for me, and he insisted it wasn’t about trust.  He said he trusts me, but not those involved in the relationship.  I know who I am, and I know I can keep such relationships my exes without being intimate with them.
However, my husband doesn’t seem to agree with me.  I don’t want to stir up any misunderstanding and arguments in my new marriage, so I have agreed to put a stop to all the friendships I currently maintain with my exes.
My question and the big debate is; is it possible for one to maintain a genuine friendship with an ex? Or do you think it is just a matter of time and something disastrous would happen when one keeps exes as friends?
Have you been able to keep exes as friends?  What happened? What is your take on this?