Learning interpretable and disentangled representations of data is a key topic in machine learning research. Variational Autoencoder (VAE) is a scalable method for learning directed latent variable models of complex data. It employs a clear and interpretable objective that can be easily optimized. However, this objective does not provide an explicit measure for the quality of latent variable representations which may result in their poor quality. We propose Variational Mutual Information Maximization Framework for VAE to address this issue. In comparison to other methods, it provides an explicit objective that maximizes lower bound on mutual information between latent codes and observations. The objective acts as a regularizer that forces VAE to not ignore the latent variable and allows one to select particular components of it to be most informative with respect to the observations. On top of that, the proposed framework provides a way to evaluate mutual information between latent codes and observations for a fixed VAE model. We have conducted our experiments on VAE models with Gaussian and joint Gaussian and discrete latent variables. Our results illustrate that the proposed approach strengthens relationships between latent codes and observations and improves learned representations.