Hosting a boy-girl playdate isn't that different from same-gender ones. For a successful get-together:
Treat it like any other playdate. When you call the other parent to make plans, you may feel like you're promoting a romance between the kids. But say matter-of-factly, "It looks like Joey and Paige have become friendly. We would love to have her over to play."
Plan activities both genders will enjoy. Boys and girls tend to like outdoor activities, like swimming and running around, so encourage those; in cooler weather, break out board games or find activity ideas on sites like funplaydates.com.
Don't call them "boyfriend and girlfriend." It may sound cute, but it can embarrass your child. If he (or someone else) uses those words, rephrase with "Isn't it nice to have Hannah as your friend?"