In reply to marcoevich.

I'll update the docs to include examples of searching for multiple.

Searching through post types works just fine, in this example I passed "type="ideas"" and its returning the first 20 results found for the "ideas" post type. http://cl.ly/image/3j3d1k2e3W1A

It returns whatever the REST API returns, which theoretically returns the same result as yoursite.com?s=test

You can test the REST API response this by appending the following to your sites url in your browser bar:
wp-json/posts?type=MYPOSTTYPE&filter[s]=test