Online social networks, World Wide Web, media and technological networks, and other types of so-called information networks are ubiquitous nowadays. These information networks are inherently heterogeneous and dynamic. They are heterogeneous as they consist of multi-typed objects and relations, and they are dynamic as they are constantly evolving over time. One of the challenging issues in such heterogeneous and dynamic environments is to forecast those relationships in the network that will appear in the future. In this paper, we try to solve the problem of continuous-time relationship prediction in dynamic and heterogeneous information networks. This implies predicting the time it takes for a relationship to appear in the future, given its features that have been extracted by considering both heterogeneity and temporal dynamics of the underlying network. To this end, we first introduce a feature extraction framework that combines the power of meta-path-based modeling and recurrent neural networks to effectively extract features suitable for relationship prediction regarding heterogeneity and dynamicity of the networks. Next, we propose a supervised non-parametric approach, called Non-Parametric Generalized Linear Model (NP-GLM), which infers the hidden underlying probability distribution of the relationship building time given its features. We then present a learning algorithm to train NP-GLM and an inference method to answer time-related queries. Extensive experiments conducted on synthetic data and three real-world datasets, namely Delicious, MovieLens, and DBLP, demonstrate the effectiveness of NP-GLM in solving continuous-time relationship prediction problem vis-a-vis competitive baselines