Articulatory information can effectively model variability in speech and can improve speech recognition performance under varying acoustic conditions. Learning speaker-independent articulatory models has always been challenging, as speaker-specific information in the articulatory and acoustic spaces increases the complexity of the speech-to-articulatory space inverse modeling, which is already an ill-posed problem due to its inherent nonlinearity and non-uniqueness. This paper investigates using deep neural networks (DNN) and convolutional neural networks (CNNs) for mapping speech data into its corresponding articulatory space. Our results indicate that the CNN models perform better than their DNN counterparts for speech inversion. In addition, we used the inverse models to generate articulatory trajectories from speech for three different standard speech recognition tasks. To effectively model the articulatory features' temporal modulations while retaining the acoustic features' spatiotemporal signatures, we explored a joint modeling strategy to simultaneously learn both the acoustic and articulatory spaces. The results from multiple speech recognition tasks indicate that articulatory features can improve recognition performance when the acoustic and articulatory spaces are jointly learned with one common objective function.