Fusarium head blight (FHB) is a devastating fungal disease of both durum and common wheat. Multiple sources of FHB resistance have been found in common wheat, but not in durum wheat. Lack of effective FHB resistance sources and complex inheritance of FHB resistance genes in durum limit the development of FHB-resistant durum varieties. This research aimed to map FHB resistance genes and to understand the inheritance of the hexaploid wheat-derived FHB resistance genes in durum. Molecular mapping positioned the wild emmer wheat (Triticum dicoccoides)-derived FHB resistance QTL Qfhs.ndsu-3AS to a chromosomal interval of 5.2 cM flanked by the molecular marker Xwgc501 and Xwgc510 on the short arm of chromosome 3A (3AS). This study reduced the linkage drag associated with Qfhs.ndsu-3AS and developed new molecular markers to assist its selection breeding. The FHB resistance genes in common wheat ‘Sumai 3’ were normally expressed in the F1 with hexaploids, but not in the F1 with durum. The common wheat PI 277012-derived FHB resistance gene(s) exhibited complete dominance in the F1 with durum. In addition, ‘Langdon’ (LDN) chromosomes 2B, 3A, 3B, 4A, 4B, 5B, 6A, 6B, and 7A were found to contain genes that suppress expression of the Sumai 3-derived FHB resistance genes in the F1, and 4A, 6A, and 6B contain genes required for expression of the PI 277012-derived FHB resistance genes in the F1. Apparently, Sumai 3-derived FHB resistance genes exhibited a more complex inheritance pattern than PI 277012 in durum. Evaluation of LDN-‘Chinese Spring’ (CS) D-genome disomic substitution lines and LDN-Aegilops tauschii D-genome addition lines for FHB resistance indicated that LDN chromosome 5A and CS chromosome 6D may contain genes for FHB susceptibility and/or suppression of FHB resistance. LDN chromosome 2B and Ae. tauschii 5D may carry genes for FHB resistance. Addition of the entire D genome to LDN increased susceptibility to FHB. Multiple LDN durum and D-genome chromosomes were identified to have either negative/suppression or positive/enhancement effects on FHB resistance. Thus, special genetic manipulation is needed to eliminate the genes with negative/suppression effects and to ensure normal expression of FHB resistance genes in durum.