I like this idea as well, and first encountered it at this site:

http://www.dprvoting.org/

Their system is called "Direct Party and Representative Voting" (DPR Voting) and it has some weird edge cases (like dealing with independent candidates, or parties that win a big vote share but no actual seats), but it definitely seems like an improvement over FPTP, and uses a very easy/quick ballot counting process (unlike IRV or Approval voting, for example).