I have cast Warding bond on a party member and then blinked into the ethereal plane via the Blink spell. If he gets hit with a non magical melee attack, would I still take damage? Also, would I still be considered 60 feet away from him if I was in the ethereal plane?
You still take damage while blinked.
Here are the relevant portions of the spell descriptions, with my emphasis added:
Blink: (PHB, p. 219)
While on the Ethereal Plane, you can see and hear the plane you originated from, which is cast in shades of gray, and you can’t see anything there more than 60 feet away. You can only affect and be affected by other creatures on the Ethereal Plane. Creatures that aren’t there can’t perceive you or interact with you, unless they have the ability to do so.
This implies that there is a spatial relationship between locations in the Ethereal plane and the caster's plane of origin that can be measured in terms of conventional distances.
Warding Bond: (PHB, p. 287)
This spell wards a willing creature you touch and creates a mystic connection between you and the target until the spell ends. While the target is within 60 feet of you, it gains a +1 bonus to AC and saving throws, and it has resistance to all damage. Also, each time it takes damage, you take the same amount of damage.
The spell ends if you drop to 0 hit points or if you and the target become separated by more than 60 feet.
This doesn't specify that the caster and target need to be on the same plane, just that they are within 60 feet. The wording of blink establishes that distances between the blinked caster's position in the Ethereal and their originating plane can be measured linearly. This interpretation depends somewhat on interpreting "separated by more than 60 feet" as meaning "linearly separated by a distance greater than 60 feet", which doesn't seem unreasonable; see below for the implications of another interpretation.
This is also established by the description of the Ethereal Plane in the PHB (p. 301):
The Ethereal Plane is a misty, fog-bound dimension that is sometimes described as a great ocean. Its shores, called the Border Ethereal, overlap the Material Plane and the Inner Planes, so that every location on those planes has a corresponding location on the Ethereal Plane.
Putting it all together, warding bond continues to operate if the caster's location in the Ethereal Plane is within 60 feet of the point in the Ethereal Plane corresponding to the location of the target.
However: A DM might interpret the phrase "separated by more than 60 feet" to mean that any planar boundary, regardless of spatial correspondence, is "more than" normal linear separation. That is, that "more than 60 feet" means "anything other than 60 feet or less of spatial distance". Even though warding bond doesn't explicitly say that it is broken if the caster and target are on different planes, that could still be construed from this sentence.
You would not take damage
The Blink spell specifically states,
You can only affect and be affected by other creatures on the Ethereal Plane. Creatures that aren’t there can’t perceive you or interact with you, unless they have the ability to do so.
This means that the attacker would not be able to damage you through the warding bond, since that would construe affecting you. It's possible that other methods of being in the Ethereal plane would allow this to function, but the Blink spell does not.