There are two types of "separate payments", don't confuse the two issues.
Firstly, if you qualify for a payment in your own right, for example if you are genuinely seeking and available for full time work, and meet all the criteria of the scheme, then you can put in a claim for Jobseekers Allowance. If he is also getting Jobseekers Allowance, then you would come off his claim, and they would split the total amount between the two of you. Its slightly different if he is on a Benefit claim, eg. Jobseekers Benefit or Illness Benefit.
If you put your own claim in, then you have to sign on in the same way as your husband and can be called in to interviews etc. You would also be on the live register and have access to all the schemes that are available to those in receipt of a Jobseekers payment.
The second option is where you stay as a qualified adult on your husband's claim (eg, if you are not looking for work yourself), but you feel that your husband is not giving you an equal share of the social welfare payment and that the money is not being used to support the family. Your claim doesn't change, you don't have to sign on, but they split the main payment between you and your husband and then pay one or other of you the increase for any children (usually the mother). This second option is what is explained in the link provided above.