You can take them together but it's best to space them out because of the problems it can cause your stomach like heartburn and so on but i would wait a coupe hours between each.
Doxycycline100 belongs to the group of medicines called tetracycline antibiotics. When you take this medication make sure that you follow the directions as you should not be taking antacids or drinking milk, yogurt and taking vitamins for a few hours before and after taking the drug.
There should be an instructions leaflet that came with your medicine, but if not, then contact and speak with the pharmacist.
Ibuprofen is an anti-inflammatory drug and the 800 dose is quite strong. This drug can upset the stomach and should be taken with or after food. Some doctors prescribe omeprazole to protect the stomach when taking Ibuprofen, but if you are using the Doxycycline, you will not be able to have any antacids.
If your doctor has prescribed you with these medications, he/she should have instructed you on how to correctly take them.
As you have to take the Doxy with food and drink a glass of water with it, you should be OK taking the Ibuprofen at the same time. Or stagger it, so that you take the Ibuprofen say an hour or two afterwards with food.
Please read the leaflet carefully that came with the Doxy, and it you have any queries (which you do have) with the regard to taking either medicine and taking them at the same time, then I would advise that you speak with the doctor that prescribed the medication or your pharmacist. Don't forget to tell them of any other medications that you are taking be it on prescription or over the counter, including any minerals and vitamin supplements.
Best wishes.