Can you recommend Jazz for some one that doesn't like Jazz?

Stuartk did an excellent job describing improvisation in jazz.  It is a lot of fun following how the ensemble weaves its way through a tune, particularly where that tune seems almost, but not totally, unrecognizable.  I suggest listening to Lester bowie’s outrageous, joyous and silly romp through the song “The Great Pretender.”  Even where it seems to have devolved into noise, you can still hear the tune and enjoy what the band is doing.

Here are some classic Bossa Nova titles which go down very smoothly:

Stan Getz / Charlie Byrd - Jazz Samba

Stan Getz / Luis Bonfa - Jazz Samba Encore!

Stan Getz / João Gilberto - Getz / Gilberto

The Modern Jazz Quartet 'Pyramid' or 'the last concert', but just about all their stuff is good.

I find they have some structure in their compositions and since you said you don't like disjointed; this may well be your cuppa.. 

The Dave Brubeck 'Tine out' suggestion is also in this vein, I believe the general category for this type of jazz is California Cool.

I like the MJQ recommendations made above, but, they may not be as accessible as the "Time Out' recommendation.  Still, it is hard to say what will connect with any one listener.  I had a friend who I lent some jazz CDs to as an introduction.  Just as a joke, I included Coltrane's "Interstellar Space" and it turned out to be the album he most liked.

I also like the suggest Samba recordings.  There is a lot of interesting South American jazz worth exploring.  I recommend Gato Barbieri's "Latin America: Chapter 1."  The track named "India" is a good track to sample.