Have you overwatered your parsley? Herbs in general do not need too much water.

Bamboo is the anthurinum expert.

Has your parsley flowered? It usually dies off after flowering.

Also, has it had regular feeding? Parsley doesn't need a lot of food, but soil in a pot can become impoverished quickly.

I haven't been able to find out what a "luxury" Anthurium is, but here are the instructions for Anthuriums in general:
Light~ medium to high indirect light, generally no direct sunlight.
Water~ moderate watering--let the top cm go dry between soakings.
Feeding~ a 3-1-2 proportioned (18-6-12, for example) houseplant food, according to package directions.
Humidity~ moderate, for A. hookeri and kin, and A. scerzerianum; and high for most other species,especially A. andreanum hybrids, and A. crystallinum.

You might want to google these species, and see which is the one that yours most resembles.