Casselman defined the real Jacquet module for a HarishChandra module, if we view the Jacquet module as a module corresponding to the Levi subgroup, the question is is it still a HarishChandra module? In particular is it still admissible?
As I understand it, the Jacquet module for $(\mathfrak g, K)$modules is defined so as to again be a $\mathfrak g$module, and in fact it is a HarishChandra module, not for $({\mathfrak g},K)$, but rather for $(\mathfrak g,N)$ (where $N$ is the unipotent radical of the parabolic with respect to which we compute the Jacquet module). (I am probably assuming that the original $(\mathfrak g, K)$module has an infinitesimal character here.) I am using the definitions of this paper, in particular the discussion of section 2. This in turn refers to Ch. 4 of Wallach's book. So probably this latter reference will cover things in detail. Added: I may have misunderstood the question (due in part to a confusion on my part about definitions; see the comments below), but perhaps the following remark is helpful: If one takes the Jacquet module (say in the sense of the above referenced paper, which is also the sense of Wallach), say for a Borel, then it is a category {\mathcal O}like object: it is a direct sum of weight spaces for a maximal Cartan in ${\mathfrak g},$ and any given weight appears only finitely many times. (See e.g. Lemma 2.3 and Prop. 2.4 in the above referenced paper; no doubt this is also in Wallach in some form; actually these results are for the geometric Jacquet functor of that paper rather than for Wallach's Jacquet module, but I think they should apply just as well to Wallach's. Maybe they also apply with Casselman's definition; if so, doesn't this give the desired admissibility? 

