D

Step 1: Understand the definition of mutual inductance. Mutual inductance is a measure of the ability of one coil to induce electromotive force (EMF) in another coil when the current in the first coil changes.
Step 2: The formula for mutual inductance (M) is given by:
$$ M = \frac{\Phi}{I} $$
where \( \Phi \) is the magnetic flux through one coil due to the current in the other coil and \( I \) is the current flowing in the first coil.
Step 3: The unit of magnetic flux \( \Phi \) is the weber (Wb) and the unit of current \( I \) is the ampere (A). Therefore, the unit of mutual inductance can be derived as follows:
$$ M = \frac{\text{weber}}{\text{ampere}} = \text{henry} \; (H) $$
Step 4: Thus, the unit of mutual inductance is the henry (H).
Therefore, the correct answer is D: henry.