It might sound unpleasant, however it can be done. Various other pairs have chosen to just consist of the names of their birth parents, referencing their existing last names. That functions just as well.
If the bride or groom's parents are divorced and you want to include both as hosts, you can include them all, just keep your each parent on a separate line. If you're going to include the name of stepparent, keep it on the same line. It might seem complex at first, but all it requires is a few more lines. This is an example of a bride with divorced (and remarried) parents' wedding invitation wording:
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