Congenital heart disease (CHD) is one of the most common birth defects. More than 200 susceptibility loci have been identified for CHDs, yet a large part of the genetic risk factors remain unexplained. Monozygotic (MZ) twins are thought to be completely genetically identical; however, discordant phenotypes have been found in MZ twins. Recent studies have demonstrated genetic differences between MZ twins. We aimed to test whether copy number variants (CNVs) and/or genetic mutation differences play a role in the etiology of CHDs by using single nucleotide polymorphism (SNP) genotyping arrays and whole exome sequencing of twin pairs discordant for CHDs. Our goal was to identify mutations present only in the affected twins, which could identify novel candidates for CHD susceptibility loci. We present a comprehensive analysis for the CNVs and genetic mutation results of the selected individuals but detected no consistent differences within the twin pairs. Our study confirms that chromosomal structure or genetic mutation differences do not seem to play a role in the MZ twins discordant for CHD.