Does Jonson's "To Celia" have regular rhyme or metre?

It's written in alternating lines of tetrameter and trimeter (that is, a line with four stresses, and a line with three stresses). I've put the scansion below (x is a strong stress, and - is a weak stress).

Drink to me only with thine eyes,
  -     x   -   x  -   x      -       x
And I will pledge with mine:
  -   x  -       x      -       x

And rhyme wise, you analyse rhyme assigning the same letter to rhyming lines. Like this:

Drink to me only with thine eyes,        A
And I will pledge with mine:                B
Or leave a kiss but in the cup,            C
And I'll not look for wine.                   B

The thirst that from the soul doth rise  A
Doth ask a drink divine                       B
But might I of Jove's nectar sup,          C
I would not change for thine.              B

I sent thee late a rosy wreath,            D
Not so much honoring thee,                E
As giving hope that there                   F
It could not withered be                     E

But thou thereto didst only breathe         D
And sent it back to me;                        E
Since when it grows and smells, I swear,  F
Not of itself, but thee.                          E

See how it works? So the recurring rhyme scheme of the poem is ABCB.