Septoria tritici blotch (STB) is a major disease problem of wheat worldwide. To optimize the introgression of resistance genes in elite genotypes throughout traditional or molecular breeding programs, a full understanding of the quantitative inheritance of resistance to Zymoseptoria tritici, plant height (PH), and thousand kernel weight (TKW) is needed. In this study, maternal and cytoplasmic effects of resistance to STB were investigated using P1 (susceptible, high-yielding line) and P2 (resistant, low-yielding line) durum wheat lines and their F1, RF1, F2, RF2, BC1, RBC1, BC2, and RBC2 progeny, assessed for resistance to STB during three growing seasons. Duncan mean’s analysis revealed significant differences between generation means for STB, PH, and TKW. The two parents had an extreme pattern. The F1 and RF1 segregated close to their respective parents, suggesting the presence of cytoplasmic and maternal genetic effects for Z. tritici resistance, PH, and TKW. Separate generation mean’s analysis confirmed the results of the Duncan test. A three-parameter model was found to be not adequate for all traits in all three growing years; while a digenic epistatic model with cytoplasmic or/and maternal effect was adequate for all cases. Narrow-sense heritability was in the range of 50–60%, 30–69%, and 28–31% for STB, PH, and TKW, respectively. For STB, high heritability and the presence of fixable epistatic effect is encouraging and could lead to creating varieties with the right female parent to exploit cytoplasmic and maternal effects in order to improve resistance to Z. tritici in durum wheat.