Diffusion-based molecular communication has become a promising scheme for communication between nanoscale devices, and various modulation schemes have recently been proposed, including type, quantity, and concentration modulation. In this paper, a novel approach of using both quantity and type of molecules to convey information is considered. An asynchronous threshold-based detection algorithm, called count-to-a-threshold (CTAT), is proposed and compared to the baseline detection approach of majority-counting (MC), which simply counts and compares the number of each type of molecule received. The MC detection algorithm, although straightforward and simple, cannot deliver satisfactory performance under the diffusion channel due to the randomness of the arriving time of molecules. On the other hand, the proposed CTAT detection, which exploits properties of the diffusion channel, greatly improves the performance of quantity-type-modulated diffusion-based molecular communication systems. Both simulations and theoretical analysis are conducted to confirm the effectiveness of the proposed CTAT detection scheme with and without background noise. Based on the analysis, guidelines to design proper molecule quantities, bit intervals, and block sizes to optimize the CTAT detection system are provided.