The recent advances in high-throughput single-cell sequencing has significantly required computational models which can address the high complexity of single-cell multiomics data. Meticulous single-cell multiomics integration models are required to avoid biases towards a specific modality and overcome the sparsity. Batch effects obfuscating biological signals must also be taken into account. Here, we introduce a new single-cell multiomics integration model, Single-cell Multiomics Autoencoder Integration (scMaui) based on stacked variational encoders and adversarial learning. scMaui reduces the dimensionality of integrated data modalities to a latent space which outlines cellular heterogeneity. It can handle multiple batch effects independently accepting both discrete and continuous values, as well as provides varied reconstruction loss functions to cover various assays and preprocessing pipelines. We show that scMaui accomplishes superior performance in many tasks compared to other methods. Further downstream analyses also demonstrate its potential in identifying relations between assays and discovering hidden subpopulations.