Finger-vein verification is a highly secure biometric authentication that has been widely investigated over the last years. One of its challenges, however, is the possible degradation of image quality, that results in spurious and missing vein patterns, which increases the verification error. Despite recent advances in finger-vein quality assessment, the proposed solutions are limited as they depend on human expertise and domain knowledge to extract handcrafted features for assessing quality. We have proposed, recently, the first Deep Neural Network (DNN) framework for assessing finger-vein quality, that does not require manual labeling of high and low quality images, as is the case for state of the art methods, but infers such annotations automatically based on an objective indicator, the biometric verification decision. This framework has significantly outperformed the existing methods, whether the input image is in grayscale or is binary. Motivated by these performances, we propose, in this work, a representation learning of finger vein image quality, where a DNN takes as input conjointly the grayscale and binary versions of the input image to predict vein quality. Our model allows to learn the joint representation from grayscale and binary images, for quality assessment. The experimental results, obtained on a large public dataset, demonstrates that our proposed method accurately identifies high and low quality images, and outperforms other techniques in terms of equal error rate (EER) minimization, including our previous DNN models, based either on grayscale or binary input.