Meiosis is one of the most conserved molecular processes in eukaryotes. The fidelity of pairing and segregation of homologous chromosomes has a major impact on the proper transmission of genetic information. Aberrant chromosomal transmission can have major phenotypic consequences, yet the mechanisms are poorly understood. Fungi are excellent models to investigate processes of chromosomal transmission, because many species have highly polymorphic genomes that include accessory chromosomes. Inheritance of accessory chromosomes is often unstable and chromosomal losses have little impact on fitness. We analyzed chromosomal inheritance in 477 progeny coming from two crosses of the fungal wheat pathogen Zymoseptoria tritici. For this, we developed a high-throughput screening method based on restriction site-associated DNA sequencing that generated dense coverage of genetic markers along each chromosome. We identified rare instances of chromosomal duplications (disomy) in core chromosomes. Accessory chromosomes showed high overall frequencies of disomy. Chromosomal rearrangements were found exclusively on accessory chromosomes and were more frequent than disomy. Accessory chromosomes present in only one of the parents in an analyzed cross were inherited at significantly higher rates than the expected 1:1 segregation ratio. Both the chromosome and the parental background had significant impacts on the rates of disomy, losses, rearrangements, and distorted inheritance. We found that chromosomes with higher sequence similarity and lower repeat content were inherited more faithfully. The large number of rearranged progeny chromosomes identified in this species will enable detailed analyses of the mechanisms underlying chromosomal rearrangement.