RECURRING contribution and auto-renew membership
If you are on Drupal, then webform_civicrm can indeed mix and match different monies [Membership + Contribution + Event] and since recently construct a recurring series as well. There are some differences though compared to how each of these individual bits work using CiviCRM Core itself:


you will add up all components using webform elements -> to get a
Total $ amount; 
you can then present to the user (or config them
yourself) - how you want these to be paid (now, monthly installments,
etc) 
you end up with one payment - and since CiviCRM Core is not really expecting that this is possible, you won't see the distribution of that payment in the backend. So a $100 contribution + $50 Membership will show $150 payment both on the Contribution screen as well as on the Membership screen.