The cell organelle that surrounds the nuclear membrane is the endoplasmic reticulum (ER). Specifically, it's the rough endoplasmic reticulum (RER) that directly surrounds the nuclear membrane.

Here's why:

* Rough ER: This type of ER is studded with ribosomes, giving it a rough appearance. It plays a crucial role in protein synthesis and folding. The RER is directly connected to the nuclear membrane, allowing for the transport of newly synthesized proteins from the nucleus to the ER.

* Smooth ER: This type of ER lacks ribosomes and is involved in lipid synthesis, detoxification, and calcium storage. While it is connected to the RER, it doesn't directly surround the nuclear membrane.

So, while both types of ER are part of a continuous network within the cell, it's the RER that physically surrounds the nuclear membrane.