First a word of caution - if you are sensitive to poison ivy, or even unsure, then leave well alone. It's not worth it for a few raspberries.
Poison ivy and raspberries are strongly surface rooted plants and exposure to the sap in cut ivy roots will trigger sensitivity. Roots spread widely and may be present even where there appears to be no top growth. So an attempt to dig out raspberries in what appears to be a clear patch might or might not expose ivy roots.
Fortunately it is easy to distinguish ivy roots from raspberry roots. The ivy will be smoothly woody sending up occasional shoots to become above ground stems. The raspberries will be mainly in tight crowns sending up bristly shoots to become canes. If you cannot distinguish them in an immature stage then best leave it alone.
Poison ivy likes to grow among other plants, so it is not surprising to find it alongside raspberries. It grows low unless the vining variety, and likes shaded to partly shaded areas like forest edges. However the presence of ivy also means the raspberries are in the wrong place; they will do a lot better in a more open sunny location.
If the raspberries are the black, tip rooting type then it is easy to get more plants from the raspberries without digging. Then plant the offshoots in a sunnier location.
Regulations regarding the chemical elimination of pests such as poison ivy vary locally, so check with your farm/garden supplier to see what options are available to you in your area. Personally I am not (so far) sensitive and have found that frequent mowing provides good control. A longer term non-chemical approach would be to eliminate the shade, suppressing the ivy and encouraging the raspberries.
When in doubt leave poison ivy alone and warn your guests of the presence.