The benefits of the contact splitting principle of bioinspired dry adhesion systems for reversible and temporary attachment to hard objects with smooth surfaces have already been demonstrated in many cases. However, the adhesion on objects with rough surfaces is still a big challenge that requires new concepts. Towards this goal, we created cylindrical two-material composite pillar structure inspired by the material gradient found on hairy ladybug feet. The composite structures are composed of a mechanically stiff stem combined with a soft tip. Our findings provide evidence that the adhesion of the composite pillar structures can exceed the adhesion of conventional pillar structures both on smooth and on rough glass substrates by a factor of about three. The adhesion characteristics can be further tuned by changing the ratio of the elastic modulus of the materials, the interface curvature and the thickness of the softer part in a way that pull-off stresses on rough glass are even in a similar range to those found on smooth glass. The experimental results are in good agreement with numerical simulations predicting an increase of adhesion energy by diminishing the corner stress singularity due to the materials interface design inside the composite. In summary, our proposed approach has the potential to be transferred into fields of application where rough surfaces are omnipresent.