The Collaborative International Dictionary of English v.0.48:

Admissibility \Ad*mis`si*bil"i*ty\, n. [Cf. F.
   admissibilit['e].]
   The quality of being admissible; admissibleness; as, the
   admissibility of evidence.
   [1913 Webster]

WordNet (r) 3.0 (2006):

admissibility
    n 1: acceptability by virtue of being admissible [ant:
         inadmissibility]

Moby Thesaurus II by Grady Ward, 1.0:

92 Moby Thesaurus words for "admissibility":
   acceptability, adequacy, adequateness, admissibleness, admission,
   agreeability, allowableness, applicability, appositeness,
   appropriateness, aptitude, aptness, assimilation, common sense,
   completeness, comprehension, comprehensiveness, comprisal,
   coverage, defensibility, eligibility, embodiment, embracement,
   encompassment, envisagement, excusability, exhaustiveness,
   explainability, explicability, fairishness, felicity, fitness,
   fittedness, forgivableness, goodishness, hospitality, inclusion,
   inclusiveness, incorporation, invitingness, justifiability,
   justifiableness, justness, lawfulness, legality, legitimacy,
   licitness, logic, logicality, logicalness, membership, openness,
   pardonableness, participation, passableness, permissibility,
   permissibleness, plausibility, propriety, qualification,
   rationality, reason, reasonability, reasonableness, reception,
   receptiveness, receptivity, recipience, relevance, remissibility,
   sanctionableness, satisfactoriness, sense, sensibleness,
   sound sense, soundness, sufficiency, suitability, sweet reason,
   tenability, tolerability, tolerableness, tolerance, toleration,
   unexceptionability, unobjectionability, validity, veniality,
   viability, vindicability, warrantableness, whole