This　article　considers　a　class　of　hyperbolic-parabolic　partial　differential　equation　(PDE)　system　with　some　interior　mixed-coupling　terms,　a　rather　unexplored　family　of　systems.　The　family　of　systems　we　explore　contains　several　interior-coupling　terms,　which　makes　controller　design　more　challenging.　Our　goal　is　to　design　a　boundary　controller　to　exponentially　stabilize　the　coupled　system.　For　that,　we　propose　a　controller　whose　design　is　based　on　the　backstepping　method.　Under　this　controller,　we　analyze　the　stability　of　the　closed　loop　in　the　$H＜^＞{1}$　sense.　A　set　of　(highly　coupled)　backstepping　kernel　equations　is　derived,　and　their　well-posedness　is　shown　in　the　appropriate　spaces　by　an　infinite　induction　energy　series,　which　has　not　been　used　before　in　this　setting.　Moreover,　we　show　the　invertibility　of　transformations　by　displaying　the　inverse　transformations,　as　required　for　closed-loop　well-posedness　and　stability.　Finally,　a　numerical　simulation　is　implemented,　and　the　result　illustrates　that　the　control　law　designed　by　the　backstepping　transformation　can　stabilize　the　mixed　PDE　system　exponentially.