We often use the term "triple point" to refer to the intersection of only two fronts or boundaries, even though the TP strictly refers to the intersections of three different airmasses (as Rich noted). This can be a dryline abutting a warm front (continental polar airmass ahead of warm front, maritime tropical south of front and ahead of dryline, and continental tropical behind the dryline), or a cold front abutting a warm front (not-terribly-cool cP N of warm front, mT south of warm front, and cP behind cold front). In the first example, the separation between the cP N of the warm front and the cT behind the dryline is often marked by a cold or stationary front; in the second example, there may be a front of some sort separating the not-terribly-cool cP N of the warm front with the relatively cold cP airmass behind the cold front. In either case, we're not very concerned about this particular front or boundary, since it's typically well removed from the potential instability in the warm / moist sector.
Of course, actual surface analyses may reveal a much more complex situation with multiple fronts (perhaps multiple warm or cold fronts, an occluded front, and one or more drylines), so it can be tricky at times! In Andy's example above, the "triple point" that chasers are most likely to refer to the intersection of the hot/dry (cT), warm/moist (mT), and cool/dry (cP) airmasses in northwestern Kansas (marked where the dryline meets the warm front). Here, we see that there *are* three airmasses "intersecting", even though there are only two boundaries involved. There looks to be another triple point back in extreme northeastern Colorado, but that is typically not going to be of interest to chasers considering the air ahead of the cold front is warm but dry (e.g. more characteristic of a cT airmass).