Children of Cohen married to convert

If a Cohen marries a convert, i realize that he loses his Cohen status, but what are the kids considered? For example, celebrity Sacha Cohen married Isla Fisher after she converted, and they have kids. So clearly it can be done since a rabbi married them. However, my question is what are the kids considered? Are they mamzerim? Thanks!

The children are not Mamzerim but are Chalalim. They can marry a Jew who is not a Cohen. From the marriage and onwards the father cannot Duchan. Rabbi Yitzchak Grinblat