In this paper, we approach the problem of minimizing the global Equal Error Rate (EER) in a Writer-Independent (WI) Online Signature Verification (OSV) system by decomposing it into two components: the separation error and the alignment error. The separation error arises from the lack of a correct separation between genuine and forged signatures, while the alignment error arises from the inability of a single global threshold to effectively capture the writer-specific separations. To this, we propose HoLoSig, a novel framework that integrates two popular deep signature representations via a shared 1D convolutional backbone that bifurcates into two specialized branches. On one branch, we employ Triplet Loss with Soft-DTW to learn variable-length local representations whose dissimilarity scores are shifted to a common region with the help of the Maximum Mean Discrepancy (MMD) to improve the system’s performance when using a global threshold. On the other branch, we employ Poly-1 Cross Entropy Loss to learn fixed-length holistic representations that are used to further boost the separation created by the local representation branch. HoLoSig achieves state-of-the-art results on DeepSignDB, the largest OSV dataset to date, against skilled and random forgeries in the stylus scenario, with EERs of 1.73% (4vs1 skilled), 3.29% (1vs1 skilled), 0.43% (4vs1 random) and 0.89% (1vs1 random). The source code is available at https://github.com/DYosplay/HoLoSig .