The wetting of rough honeycomb micrometrically scaled polymer substrates was studied. A very strong dependence of the apparent contact angle on the drop volume has been established experimentally. The environmental scanning electron microscopy study of the fine structure of the triple line is reported first. The triple line is not smooth and prefers grasping the polymer matrix over air holes. The precursor rim surrounding the drop has been observed. The revealed dependence of the apparent contact angle on the drop volume is explained by the transition between the pure Cassie and combined Wenzel-Cassie wetting regimes, which is induced by capillarity penetration of water into the holes of relief.