In nanoscale communication, diffusion-based molecular communication (DBMC) in which information is encoded into molecule patterns by a transmitter nanomachine, has emerged as a promising communication system, particularly for biomedical and healthcare applications. Although, numerous studies have been conducted to evaluate and analyze DBMC systems, investigation on DBMC system through a multilayer channel has received less attention. The aims of this paper are to formulate channel characteristics and to evaluate the performance of multilayer DBMC channel in terms of delay spread and capacity. In this paper, the propagation of molecules over an n- layer channel is assumed to follow the Brownian motion and subjected to Fick's law of diffusion. Fourier transform is used to convert time to frequency domain functions. Besides, the multilayer channel is considered as a linear and deterministic channel. For the performance evaluation, the air-water-blood plasma medium representing the simplified multilayer diffusion model in the respiratory system was chosen. It was found that a high channel capacity can be achieved with wide transmission bandwidth, short transmission distance, and high averaged transmitted power. In addition, the findings showed that channel delay spread increases as both the transmission distance, and the pulse duration increased. By setting the symbol duration greater than the pulse duration or delay spread, an inter-symbol interference problem due to previous molecules transmission can be mitigated. These findings can be used as a guide in the development and fabrication of future artificial nanocommunication and nanonetworks systems involving multilayer transmission medium.