We study the behavior of an ink-paper interface in a spontaneous imbibition experiment as a function of time and paper orientation. To characterize the interface roughness the growth beta and Hurst H exponents (calculated using the root mean square interface width W) and the H{q} scaling exponent (calculated using the qth order height-height correlation function) are used. Our results indicate that the values of H and H{q} depend on the orientation of the paper sheets, while beta does not, and that the interface exhibits a multiaffine character during all its evolution.