is id and phone number enough to uniquely identify a row in phone numbers
There are probably ways to solve this (e.g. an instead of trigger rather than an explicit constraint, or a clever filtered index if on 2008+), but why?

As an example, you can do this with two filtered indexes in 2008+:

CREATE TABLE #cpn(c INT, pn VARCHAR(32), x VARCHAR(8000));

CREATE UNIQUE INDEX x ON #cpn(c, pn) WHERE x IS NULL;
CREATE UNIQUE INDEX y ON #cpn(c, pn, x) WHERE x IS NOT NULL;

INSERT #cpn(c, pn   ) SELECT 1, '555-5555';        -- OK
INSERT #cpn(c, pn, x) SELECT 1, '555-5555', '345'; -- OK
INSERT #cpn(c, pn, x) SELECT 1, '555-5555', '555'; -- OK
GO
INSERT #cpn(c, pn   ) SELECT 1, '555-5555';        -- fails on index x
GO
INSERT #cpn(c, pn, x) SELECT 1, '555-5555', '345'; -- fails on index y


But I fail to see the point. This seems like unnecessary flexibility. If I'm going to call the office and try to reach Bob at extension 55, why would I be any more likely to reach him at extension 67? Does this seem like a feasible, real-world scenario to anyone?

I suggest you make it a business rule that a user can only have one extension at the same number. This way you can keep your constraint on customer id and phone number, and allow extension to be optional.

Also, assuming you are storing phone number and extensions as strings, you can go the other way and let people enter them together instead of separate. If they want to enter 15 different extensions at the same number, why stop them? I also think it's silly to allow an extension of 0, but this would allow that also.