The dizi is a traditional Chinese transverse flute and is most distinguished from the western flute by the presence of a hole covered by a wrinkled membrane. In this study, we analyze the linear acoustical behavior of the dizi resonator through a detailed acoustical model that incorporates drilled toneholes, back end-holes, membrane hole, and upstream embouchure hole. The input admittance of the dizi is measured and modeled using the Transfer Matrix Method (TMM) and Transfer Matrix Method with external Interactions (TMMI). In comparison to measurements, the TMMI is shown to more accurately model the dizi than the TMM when compared to measurements. Our analysis reveals that attaching the membrane shifts admittance peaks to lower frequencies, reduces their magnitude, and influences tuning and harmonicity for different peaks and fingerings. The study further shows that the upstream branch, which includes the embouchure hole, complicates the evaluation of the tonehole lattice cutoff frequency, suggesting that it may not need to be considered for flute instruments. Cutoff frequencies exhibit distinct groupings across fingerings, influenced by the different tonehole lattices in the dizi: finger-hole lattice and end-hole lattice.