From the Belastingdienst website (emphasis mine):
Because you reside in the Netherlands, you have to declare all of your income, even if the tax levy on that income has been designated to Belgium. However, you do not pay tax on that income twice.
We first calculate the tax on your entire income. After that, we calculate the tax that you must pay on the income that is also taxed in Belgium. For that amount, you will get a relief from the tax to be paid by you. This is called double tax relief (on the tax return notice this relief is called 'relief for taxation elsewhere').
They are the official source of information on the topic of taxation.
Regarding health insurance, you need to pay for insurance in the country where you are working. If you work in both countries, it depends on the ratio if you'll need to pay insurance in both countries. This page describes your situation in Dutch, but transcribed it comes down to:
- You live in The Netherlands;
- You work in Belgium for a Belgian company;
- You don't work in The Netherlands;
- Given these criteria, you only need to pay Belgian health insurance, which amounts to roughly € 10,- a month.
I advise you take a look at the Belastingdienst link, and browse through their other pages and see which situations apply to you.