The MCI Airport Diagram chart depicts an island behind gates 40 through 43 which is no longer present. The commercial Parking Gate Coordinates chart depicts Taxiway D ending at Taxiway L when in fact it continues to Runway 19R.

Narrative

After pushback from Gate; taxi instructions were given that seemed to conflict with a Company plane taxiing into an adjacent Gate that was behind and to the right of us. We proceeded the only direction that cleared us from the gate area and Company. The Commercial Airport charts do not depict Taxiway D or an island median on the ramp the same way which confused the real time visual picture. As I was trying to rectify the taxi clearance with the charted and actual taxiway layout; we were given a different clearance to use L; M; and B Taxiways to 19R. We were already on D passing L as previously cleared. Ground Control informed us that we had missed L and to now take D; B; and hold short of M. As the Controller commented that we missed L; I referred back to the charts and missed the hold short of M instruction while questioning myself on the chart depiction. As we proceeded on D; then B; and approaching M; Company was holding short of B on M waiting for us so there was no indication to me to hold short of M. After passing M; Ground Control informed us we were supposed to hold short of M. We apologized for the misunderstanding and proceeded with no further conflict to 19R. The taxiway charts depiction needs to be revised to avoid a confusing situation that tends to momentarily distract from the job at hand. I knew where I was on the airport and was not concerned about a runway incursion. Visibility was not an issue so the need to stop and sort out the chart confusion seemed excessive and time consuming; but it would have been the prudent thing to do. I also should have called upon my First Officer; but didn't because he was busy reworking the takeoff data due to changing weather.