The basal lamina, a specialised type of extracellular matrix (ECM) that differs between cell types, acts as a base for stratified epithelia cells to layer on top of and therefore has a supportive role as well as providing a base for attachment (for the layer of cells immediately on top of it) 1. Layers of epithelial cells on top of further strata of similar cells with no differing tissue composition underneath would have no support and cell types would be able to mix freely within tissues. The different cell types within tissues are kept seperate by this ECM to maintain areas for specific functions. The importance of this can be seen through studying epithelial cancers, where the epithelial cell layer breaks through the entire basement membrance and invades the surrounding tissue. This can cause massive disruption of tissue function.
Yes, it seems that the layers of cells are attached by various junctional complexes, the desmosomes (maculae adherentes) being the most abundant for stratified epithelia.