In this work, we introduce a novel problem setup termed as Heterogeneous Semi-Supervised Learning (HSSL), which presents unique challenges by bridging the semi-supervised learning (SSL) task and the unsupervised domain adaptation (UDA) task, and expanding standard semi-supervised learning to cope with heterogeneous training data. At its core, HSSL aims to learn a prediction model using a combination of labeled and unlabeled training data drawn separately from heterogeneous domains that share a common set of semantic categories; this model is intended to differentiate the semantic categories of test instances sampled from both the labeled and unlabeled domains. In particular, the labeled and unlabeled domains have dissimilar label distributions and class feature distributions. This heterogeneity, coupled with the assorted sources of the test data, introduces significant challenges to standard SSL and UDA methods. Therefore, we propose a novel method, Unified Framework for Heterogeneous Semi-supervised Learning (Uni-HSSL), to address HSSL by directly learning a fine-grained classifier from the heterogeneous data, which adaptively handles the inter-domain heterogeneity while leveraging both the unlabeled data and the inter-domain semantic class relationships for cross-domain knowledge transfer and adaptation. We conduct comprehensive experiments and the experimental results validate the efficacy and superior performance of the proposed Uni-HSSL over state-of-the-art semi-supervised learning and unsupervised domain adaptation methods.