Blinking to the ethereal plane does not halt the fall.
Nothing within the Blink spell or the Ethereal plane's description suggests that you lose momentum during your short existence within the Ethereal plane.
Thus, at the beginning of your next turn, your falling distance in not set to 0. Once you hit the ground, you take the full damage associated with a 510' fall.
A 'lenient' DM may reasonably apply the optional rule for falling from XGE because while you're on the ethereal plane you can basically hover/fly.
If you’d like a flying creature to have a better chance of surviving a fall than a non-flying creature does, use this rule: subtract the creature’s current flying speed from the distance it fell before calculating falling damage. This rule is helpful to a flier that is knocked prone but is still conscious and has a current flying speed that is greater than 0 feet. The rule is designed to simulate the creature flapping its wings furiously or taking similar measures to slow the velocity of its fall.
But that won't help much in this scenario because you would still take the falling damage associated with a 480' fall.
The Ethereal Plane also disobeys the laws of gravity; a creature there can move up and down as easily as walking.
...if you ready your action to move on the Ethereal plane you could reasonably halt your fall.
This is similar to what a flying creature can do according to XGE's optional rules for falling:
If you use the rule for rate of falling in the previous section, a flying creature descends 500 feet on the turn when it falls, just as other creatures do. But if that creature starts any of its later turns still falling and is prone, it can halt the fall on its turn by spending half its flying speed to counter the prone condition (as if it were standing up in midair).