Is pulmonary hypertension an inherited disease?

Sometimes. There are some forms of pulmonary HTN that are inherited and there are some conditions that lead to pul HTN that are inherited but there are also forms of pul HTN that are not inherited.
It may be inherited. Up to 5% of patients with pulmonary arterial hypertension (pah) may have a genetic or heritable cause. Research studies have identified a genetic abnormality affecting bone morphogenetic protein receptor 2 (bmpr2) that appears to predispose a patient to pah. Fortunately, even if an individual inherits the abnormal gene, the likelihood of developing pah is only 1 in 5.