The articulatory geometric configurations of the vocal tract and the acoustic properties of the resultant speech sound are considered to have a strong causal relationship. This paper aims at finding a joint latent representation between the articulatory and acoustic domain for vowel sounds via invertible neural network models, while simultaneously preserving the respective domain-specific features. Our model utilizes a convolutional autoencoder architecture and normalizing flow-based models to allow both forward and inverse mappings in a semi-supervised manner, between the mid-sagittal vocal tract geometry of a two degrees-of-freedom articulatory synthesizer with 1D acoustic wave model and the Mel-spectrogram representation of the synthesized speech sounds. Our approach achieves satisfactory performance in achieving both articulatory-to-acoustic as well as acoustic-to-articulatory mapping, thereby demonstrating our success in achieving a joint encoding of both the domains.