I want to extract projects from GitHub using qualifiers as filters and according to https://github.com/search/advanced, it seems like it is not possible to search for projects written in more than 1 languege. For example, I want to retrieve projects whose main language are java, but has a front-end written in html, javascript, and the frameworks bootstrap, jquery, etc, so the language filter should allow an "and" in the selection. Is there a good way to realize this search ?
No, not possible using search. As a workaround, you might consider fetching the list of projects for a specific language using search, and then fetch the other languages using a different API endpoint:
https://developer.github.com/v3/repos/#list-languages
Once you have that -- you can filter on your end based on the full list of languages.