Is it possible that a person have both sickle cell anaemia and thalassemia at the same time?

Yes!: Sickle cell and beta thalassemia both affect the same part of hemoglobin. If you inherit a sickle gene from one parent and a thalassemia gene from the other, you have sickle/b-thalassemia. The severity depends on whether the thal gene works a little (b+) or not at all (b0). Sickle cell and Alpha thalassemia are inherited independently; you can inherit both from the same parent or one from each.