You may be eligible for JB depending on your PRSI contributions.
If you do qualify for JB, your partner can be paid JA, though it's likely to be lower than your JB.
The total amount paid cannot exceed what one of you would get if that person claimed for both of you.
For example, the 2010 rate for a couple is 326.10. You cannot get more than 326.10 between you, so if you receive 196 JB, your partner can only receive 131.10.
The above figures will be reduced in 2011, and assume no savings or other income which may affect the JA.
You will be treated as a couple for the purposes of Rent Supplement, even if both of you are on Jobseeker's, so there is no need for both of you to apply.