In an attempt to confer robots with complex manipulation capabilities, dual-arm anthropomorphic systems have become an important research topic in the robotics community. Most approaches in the literature rely upon a great understanding of the dynamics underlying the system's behaviour and yet offer limited autonomous generalisation capabilities. To address these limitations, this work proposes a modelisation for dual-arm manipulators based on dynamic movement primitives laying in two orthogonal spaces. The modularity and learning capabilities of this model are leveraged to formulate a novel end-to-end learning-based framework which (i) learns a library of primitive skills from human demonstrations, and (ii) composes such knowledge simultaneously and sequentially to confront novel scenarios. The feasibility of the proposal is evaluated by teaching the iCub humanoid the basic skills to succeed on simulated dual-arm pick-and-place tasks. The results suggest the learning and generalisation capabilities of the proposed framework extend to autonomously conduct undemonstrated dual-arm manipulation tasks.