In linkage analysis for mapping genetic diseases, the transmission/disequilibrium test (TDT) uses the linkage disequilibrium (LD) between some marker and trait loci for precise genetic mapping while avoiding confounding due to population stratification. The sib-TDT (S-TDT) and combined-TDT (C-TDT) proposed by Spielman and Ewens can combine data from families with and without parental marker genotypes (PMGs). For some families with missing PMG, the reconstruction-combined TDT (RC-TDT) proposed by Knapp may be used to reconstruct missing parental genotypes from the genotypes of their offspring to increase power and to correct for potential bias. In this paper, we propose a further extension of the RC-TDT, called the reconstruction-combined transmission disequilibrium/heterogeneity (RC-TDH) test, to take into account the identical-by-descent (IBD) sharing information in addition to the LD information. It can effectively utilize families with missing or incomplete parental genetic marker information. An application of this proposed method to Genetic Analysis Workshop 14 (GAW14) data sets and extensive simulation studies suggest that this approach may further increase statistical power which is particularly valuable when LD is unknown and/or when some or all PMGs are not available.