Heterogeneous domain adaptation aims to exploit labeled training data from a source domain for learning prediction models in a target domain under the condition that the two domains have different input feature representation spaces. In this paper, we propose a novel semi-supervised subspace co-projection method to address multiclass heterogeneous domain adaptation. The proposed method projects the instances of the two domains into a co-located latent subspace to bridge the feature divergence gap across domains, while simultaneously training prediction models in the co-projected representation space with labeled training instances from both domains. It also exploits the unlabeled data to promote the consistency of co-projected subspaces from the two domains based on a maximum mean discrepancy criterion. Moreover, to increase the stability and discriminative informativeness of the subspace co-projection, we further exploit the error-correcting output code schemes to incorporate more binary prediction tasks shared across domains into the learning process. We formulate this semi-supervised learning process as a non-convex joint minimization problem and develop an alternating optimization algorithm to solve it. To investigate the empirical performance of the proposed approach, we conduct experiments on cross-lingual text classification and cross-domain digit image classification tasks with heterogeneous feature spaces. The experimental results demonstrate the efficacy of the proposed method on these heterogeneous domain adaptation problems.