You can. It's incredibly badly worded (either that or it's changed VERY recently but I don't think so?) I claimed full MA for my now 12 month old and my nearly 4 year old despite making a loss on my business so definitely not £30/week!! I think it's missing "or" instead of "and", or perhaps that part applies to people who were employed only.
It's bad news though if you have a small earnings exemption as that vastly reduces the amount you can claim. Nobody ever tells you that when you take it out and it caused huge issues for me when I claimed MA with DC3 back in 2011 - I had to cancel it ASAP and try and squeeze in enough weeks without it there.
Anyway, on their claim form it STILL has this to say:
"If you are self-employed
We use the earnings rule to work out your
Maternity Allowance.
If you are self-employed you are required by law to
register as self-employed
This with HM Revenue & Customs.
If you do not register, or register late, you may lose
some or all of your entitlement to Maternity Allowance.
If you
l are registered as self-employed, and
l have paid Class 2 National Insurance contributions,
and
l do not hold a Small Earnings Exception certificate
[b]you will be treated as having enough weekly earnings
to result in the standard rate of MA for any week
covered by that Class 2 National Insurance
contribution.[/b]
If you are registered as self-employed and hold a
Small Earnings Exception certificate, you will be treated
as having earnings of £30 at the end of each week
covered by the certificate. This applies even if you have
paid a Class 2 National Insurance contribution for a
week covered by the certificate.
If you have been registered as self-employed for at
least 26 weeks in your test period, you may not
qualify for MA unless
l you have paid Class 2 National Insurance
contributions in your test period, or
l you have held a Small Earnings Exception
certificate for at least 13 weeks in your test
period."
This is from here: www.gov.uk/government/uploads/system/uploads/attachment_data/file/362837/ma-print.pdf
That suggests you are eligible, just like I was.
How long have you had that certificate? I can't remember if it's 13 or 26 weeks you need without it, plus class 2 contributions.
Anyway give them a call - Jobcentre Plus.