Building on @tkellen’s reply, you can also split the query up over multiple query parameters if necessary, so the search “find me all comments which has sometext in their content and all posts that has sometext in their title” could become GET /resources?filter[comments][content][contains]=sometext&filter[posts][title][contains]=sometext.
Finally, if your searches get too complicated for query parameters, and you do have to use something like POST /searches instead, the resulting search resource can then just have a single results relationship, which can be uniformly paginated, and, as Tyler mentioned, can contain resources of more than one type.