Thanks for your query.
If the pills are being taken correctly as prescribed, they offer protection even on the week while you are taking white pills.
The kind of bleeding you describe does not sound normal, as abnormal bleeding with pills is common, but normalizes within a month of two.
It could be because the dose of the pills is not appropriate for you, or due to conditions like cervical polyps, endometrial lining overgrowth, hormonal
imbalances, polycystic ovaries
, bleeding disorders etc.
Please consult your health care provider in any case.