It sounds strange, but is partially a matter of idiosyncratic terminology.
There are three components to what you pay for a Danish morgage:
- Repayments of principal.
- "Interest", which is forwarded to the owners of the covered bonds that funded the mortgage. (This might be either a fixed rate or contractually specified to depend on interbank rates in a defined way).
- A variable administration fee ("bidrag" in Danish) to the mortgage bank that issued the mortgage and bonds.
In this case the "interest" part is negative, but the "bidrag" is still a larger and positive percentage of the principal, so the bank still makes money (and it's still a net expense for the homeowner to borrow).
The bond interest becomes negative because the bonds are considered extremely safe investments (due to strict regulation of the mortgage banks, and laws that give bond owners priority rights to the collateral in case the bank goes bankrupt) and therefore attractive especially because the central bank's current deposit rate for DKK is also negative, namely -0.65%.
See Why would one buy a bond with negative rate?
Another wrinkle to bear in mind for Danish mortgages is that the (currently negative) bond interest rate is a percentage of the nominal bond value, rather than the actual amount of money the homeowner borrowed.
When the loan is originated, the mortgage bank will sell enough bonds on the open market to raise the cash the borrower needs, but the borrower pays interest on the nominal value of those bonds, rather than the actual sale price. The coupon rate on the bonds is selected in coarse increments such that the market value of the bonds will hover just below par when they are issued. This exposes the borrower to the day-to-day market rate when the loan was originated, and means that the basis for interest calculations (and repayments) is slightly higher than the actually borrowed amount.
(The market value of the bonds cannot rise much above par, because the issuing bank has a right to do forced buybacks at par, which happens to account for ordinary repayments as well as early pay-offs).
The outcome of all this is that the nominal bond interest is not a reliable indicator of the actual cost to the homeowner. Mortgage banks are required to also quote an honest overall APR prominently in their estimates when they offer loans. In Jyske Bank's examples the APR is stated as positive values between 1.7% and 2.72% depending on principal and maturity.