The disordered ferrite system, Mn1-xZnxFe2O4 for 0<=x<=0.95 has been studied by the Mössbauer-effect technique at 4.2 K in applied magnetic fields of 50 and 90 kOe. In these fields a ferrimagnetic structure is implied for the entire family of compounds. For x=0 the cation distribution is (Mn0.82Fe0.18)[Mn0.18Fe1.82]O4; for larger x the iron concentration on A (tetrahedral) sites decreases, and becomes less than 2 at.% by x=0.6. For x>=0.6, some of the Fe ions on B (octahedral) sites have their spin moments reversed. Within the experimental error, the magnetic moments of the iron ions are collinear for x<0.5 and noncollinear for x>0.5. The canting angles for normal B-site cations are found to increase with increasing zinc content, and to depend on the applied field. The sample with x=0.80 has the most stable structure. The hyperfine fields and isomer shifts show only a small variation with sample composition.