Recently, universal neural machine translation (NMT) with shared encoder-decoder gained good performance on zero-shot translation. Unlike universal NMT, jointly trained language-specific encoders-decoders aim to achieve universal representation across non-shared modules, each of which is for a language or language family. The non-shared architecture has the advantage of mitigating internal language competition, especially when the shared vocabulary and model parameters are restricted in their size. However, the performance of using multiple encoders and decoders on zero-shot translation still lags behind universal NMT. In this work, we study zero-shot translation using language-specific encoders-decoders. We propose to generalize the non-shared architecture and universal NMT by differentiating the Transformer layers between language-specific and interlingua. By selectively sharing parameters and applying cross-attentions, we explore maximizing the representation universality and realizing the best alignment of language-agnostic information. We also introduce a denoising auto-encoding (DAE) objective to jointly train the model with the translation task in a multi-task manner. Experiments on two public multilingual parallel datasets show that our proposed model achieves a competitive or better results than universal NMT and strong pivot baseline. Moreover, we experiment incrementally adding new language to the trained model by only updating the new model parameters. With this little effort, the zero-shot translation between this newly added language and existing languages achieves a comparable result with the model trained jointly from scratch on all languages.