What application are you using to do the invoicing? The answer differs depending on whether the invoice is entered directly into AR, or if you use a different application such as OrderEntry or Invoices.
Yes, it is possible to charge different tax on the same invoice, depending on how you have set up the tax table, because each item / distribution tracks the amount of tax based on Item Tax Status in conjunction with Customer Tax Status.
Very generally for OE or IN, the Tax Table would need to have both GST and HST jurisdictions defined, and the Item Tax status would charge one tax or the other. Look at Sample Data for some ideas.
It's too much to describe how to set up tax tables on a discussion forum. To get what you specifically require, it's best to discuss with your Adagio consultant.
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Softrak Tech Support