The Shulchan Aruch (512:1) rules that one may not invite a gentile to one’s home for a Yom Tov meal. Although Halacha allows cooking on Yom Tov, one may cook on Yom Tov only for Jews; it is forbidden to cook food on Yom Tov for gentiles. The Sages therefore forbade inviting a gentile to one’s home for a Yom Tov meal, as he might then prepare food for him in violation of Halacha. Whoever says otherwise is arguing on the Shulchan Aruch.
What if there is a mixed couple and the wife is jewish and the Kids are jewish. You want to try to mekarev them, but the only way you will get them to come is also invite the non-jewish husband.