You can mark your hours as billed/billable in several ways in Timeneye.
Firstly, you can do it from the Entries list, which you can open by clicking on the Timesheet icon on the sidebar.
In the Entries list, click on the Show filters button and you'll be able to sort out your entries according to the filters until you get to the entries you need.
Select the filters. You should see the checkbox appear next to the entries;
Start selecting the entries: you should see a light blue section appear on the left. Here you can select the Billed Status of your entry ;
When you're done, click on Update entries.
Non-Billable entries in a Billable project
Are there any activities in your billable project that you'd rather leave out of your totals and not put in your client's invoice?
From the same view, you can mark an entry as non-billable even if it belongs to a billable project.