I've been diagnosed with hypoparathyroidism yet have normal calcium levels, is this normal?

Can be normal. It all depends on the severity of your parathyroid underactivity. Causes of hypoaparathyroidism can also be transient in nature. Make sure you get your magensium and vitamin d (both, 25 and 1, 25 vitamin d) levels checked and also to do 24 hr urine collection for calcium. Discuss this with your endocrinologist.