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We show that particle roughness leads to changes in the number, shape and resulting capillary force of liquid bridges in capillary suspensions. We created fluorescently labeled, raspberry-like particles with varying roughness by electrostatically adsorbing silica nanoparticles with sizes between 40 nm and 250 nm on silica microparticles. Rougher particles require more liquid to fill the surface asperities before they form pendular bridges, resulting in smaller and weaker bridges. In a system where the effective bridge volume is adjusted, higher particle roughness leads to less clustered networks, which show a higher yield strain for a matching storage modulus compared to the smooth particle networks. This finding suggests that the particle-particle frictional contacts also affects the strength of capillary suspensions. Using asymptotically nonlinear oscillatory rheology, we corroborate the non-cubical power law scaling of the third harmonic in the shear stress response that results from both Hertzian contacts and friction between particles connected by capillary bridges. We demonstrate that the repulsive Hertzian contact parameter $A$ is sensitive to the liquid bridge strength and that roughness appears to shift the relative scaling of the power law exponents from adhesive-controlled friction to load-controlled friction.