The complement of saw, Jane reading the book, is, categorially speaking, an IP whose I(nfl) head is the non-finite affix -ing, with a subject Jane in Spec I position (but not a CP, i.e., not a complete 'clause', against what jlawler's comment claims). That IP is, indeed, theta-marked by saw with the role traditionally called 'Theme'. It is not, however, Case-marked by saw, because IPs cannot absorb Case, which entails that the accusative Case feature that saw can assign remains available to be absorbed by some available DP (i.e., Jane, in this case).
As non-finite I(nfl) -ing cannot assign Case (except 'null' Case to PRO in constructions like I enjoyed [ __[PRO reading the book]], where enjoyed takes a full CP complement), in I saw Jane reading the book, Jane then 'exceptionally' receives accusative Case from saw (one of the 'exceptional Case marking' (ECM) verbs - which, at bottom, means a small number of verbs that may select IP instead of CP complements). The difference is that the DP occupying the Spec I of IP complements is not 'protected' by the CP barrier and remains accessible to Case-marking by an external verb, saw in this case, whereas the PRO subject of full CPs is inside the CP barrier and inaccessible to the higher verb (enjoyed, in my example above).
Evidence for the classical analysis just offered comes from at least two simple facts: one is that * I saw [PRO reading the book] is ungrammatical (whereas e.g. I enjoyed [__ [PRO reading the book]] is not), and it is ungrammatical because its PRO subject is doubly Case-marked (as 'null' Case by the IP-internal -ing Infl, and as accusative by the governing verb saw; the other is that when the higher verb see appears in passive form and so loses its transitivity and its capacity to assign accusative Case, as in __ was seen [__ reading the book], the lower subject Jane can no longer receive accusative Case from see and, to avoid violating the Case Filter, must raise from Spec IP into the Spec T of the main clause and become its subject, as in Jane was seen [ t reading the book]. This, in turn, entails that the ing-clause cannot have a PRO subject after ECM verbs like see, since it has a trace-of-Jane one, and so that it must be an IP, not a CP, Q.E.D.