A rapid exchange balloon dilation catheter includes a catheter shaft with a proximal tubular member defining a proximal inflation/deflation lumen for conveying fluids therethrough with a distal portion of the bore of proximal tubular member filled with a fluid-impervious barrier, a distal body extending from the fluid-impervious barrier to the distal end of the shaft, a plurality of distal tubular members defining distal inflation/deflation lumens in fluid communication with the proximal inflation/deflation lumen and extending through the fluid-impervious barrier and the distal body to the distal end of the shaft distal portion, a guidewire tubular member having a bore extending from a side aperture formed in the distal body through the distal body alongside the distal tubular members in a multi-lumen arrangement, and a plurality of stiffening members extending from within the fluid-impervious barrier into the distal body to a point within the shaft distal portion.