We have developed and successfully tested a prototype of a new type of high position resolution hybrid X-ray detector. It contains a thin wall lead glass capillary plate converter of X-rays combined with a microgap parallel-plate avalanche chamber filled with gas at 1 atm. The operation of these converters was studied in a wide range of X-ray energies (from 6 to 60 keV) at incident angles varying from 0-90 degree. The detection efficiency, depending on the geometry, photon energy, incident angle and the mode of operation, was between 5-30 percent in a single step mode and up to 50 percent in a multi-layered combination. Depending on the capillary geometry, the position resolution achieved was between 0.050-0.250 mm in digital form and was practically independent of the photon energy or gas mixture. The usual lead glass capillary plates operated without noticeable charging up effects at counting rates of 50 Hz/mm2, and hydrogen treated capillaries up to 10E5 Hz/mm2. The developed detector may open new possibilities for medical imaging, for example in mammography, portal imaging, radiography (including security devices), crystallography and many other applications.