Nano-aerosols are airborne aerosols in the range of 100 nm. They are present abundantly in both pollutants and viruses, both of which affect human health. Filtering these nano-aerosols leads to high-pressure drop in cabin filters due to their small sizes forming impermeable dust cake, and prior to cake formation the capture efficiency is rather poor with conventional microfiber filters. We have investigated a composite filter with a microfiber layer positioned immediately upstream of a nanofiber layer. Such composite filter provides high efficiency and low-pressure drop during all phases of filtration of nano-aerosols: initial depth filtration, transition, and final cake filtration. The behavior of the composite filter together with various filter benchmarks (single and composite filters of microfiber/nanofiber filters) has been investigated by monitoring the pressure drop, especially during cake filtration. Using the measurements together with Ergun/Kozeny-Carman equation and material balance we come up with a new method to determine the solid volume fraction and permeability of the cake. The grade efficiency for the most penetrating particle is also measured concurrently to define the incipient point to cake formation and provide material balance. Most importantly, for the first time we have confirmed that the cake ultimately forms on the composite filter is due to the cake that originates from the upstream microfiber layer and not from the downstream nanofiber layer. Therefore, the pressure drop for the composite filter can be sustained relatively low throughout the filtration. On the other hand, the aerosol capture efficiency stays very high from start-to-end of filtration, with high initial filtration efficiency courtesy of the nanofiber filter installed downstream of the composite filter. The price to pay is a slightly higher pressure drop for the composite filter in the clean unloaded state, but this is insignificant during aerosol loading as most pressure drop is attributed to that of the cake. For the first time we have introduced, also independently using Buckingham-Pi analysis, a brand new dimensionless parameter, Beta, which measures the equivalent "thickness" of additional cake deposition (in molten form) to the viscous flow resistance "path length" due to the additional cake deposit. A high-capacity filter aimed for heavy aerosol loading should have large Beta that results in low solidosity, high porosity, and high permeability for the cake. In our study, the microfiber-nanofiber composite filter has the highest Beta of nearly 4 and also highest efficiency. Despite high efficiency the single nanofiber filter has much lower Beta of 2, while the single microfiber filter has Beta of 3, yet much lower efficiency, especially at initial filtration. Using the microfiber-nanofiber composite filter design, we can "engineer the cake" deposited on the filter to be more permeable and with least flow resistance during aerosol loading to attain high Beta values. This is an innovative approach to increase the badly needed aerosol storage capacity with low pressure drop for the nanofiber filter while maintaining high efficiency throughout the aerosol loading for extended filtration applications. The highly permeable aerosol cake can also be cleaned by backpulsed-and-backblow readily for filter reuse.