This paper presents a novel and flexible multi-task multi-layer Bayesian mapping framework with readily extendable attribute layers. The proposed framework goes beyond modern metric-semantic maps to provide even richer environmental information for robots in a single mapping formalism while exploiting existing inter-layer correlations. It removes the need for a robot to access and process information from many separate maps when performing a complex task and benefits from the correlation between map layers, advancing the way robots interact with their environments. To this end, we design a multi-task deep neural network with attention mechanisms as our front-end to provide multiple observations for multiple map layers simultaneously. Our back-end runs a scalable closedform Bayesian inference with only logarithmic time complexity. We apply the framework to build a dense robotic map including metric-semantic occupancy and traversability layers. Traversability ground truth labels are automatically generated from exteroceptive sensory data in a self-supervised manner. We present extensive experimental results on publicly available data sets and data collected by a 3D bipedal robot platform on the University of Michigan North Campus and show reliable mapping performance in different environments. Finally, we also discuss how the current framework can be extended to incorporate more information such as friction, signal strength, temperature, and physical quantity concentration using Gaussian map layers. The software for reproducing the presented results or running on customized data is made publicly available.