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Arthur, Amanda, and son Arthur (age 3 years 11 months) are in the 1920 Census in Chicago and it says he immigrated in 1908 and was naturalized. 

They are still in Chicago in 1930, although it says Arthur immigrated in 1905.

In the 1910 Census, Arthur is single and living with 3 men listed as "partners".  They all work in a club.  It says Arthur immigrated in 1907 and was an alien.

I found him on a passenger list for the Umbria from Liverpool to NY arriving 20 Oct. 1907.  He was listed as age 25, a man servant, going to Chicago, Ill.  The writing is a bit hard to read, but it says he was going to join Mr. Palmer, 100 Lake Shore Drive, Chicago.

Per the Illinois death database, Arthur Chard Millman died 5 Jan. 1950.  http://www.cyberdriveillinois.com/departments/archives/idphdeathindex.html

It's noted here that he was naturalized:  http://www.cookcountyclerkofcourt.org/NR/about.aspx

I don't think there's anything online that lists everyone who was born/died in Albany.  Most of New York State didn't start statewide registration until the 1880's, but if the events definitely happenend in Albany, they have records dating back to 1870:  http://www.albanyny.gov/Government/Departments/VitalStatistics/Genealogy.aspx

That was from Ancestry, and I think that database requires a US subscription. 

Ancestry probably has the most comprehensive information for the US and has some free things, but it's mostly subscription.  You can search without a subscription and ask for look-ups here if you see anything that might match.  Rootsweb.com is a good free site.  usgenweb.org has lots of sites with state/local information.  You can check the US Resources section of this board for other sites that might help. 

WWI Draft Registration Card
Gavin Murray Patterson
William Hill, Monongahela, Wash Co., Pa.
Age 37, born 2 Dec. 1881
White, Alien - declarant
Occupation - clerk diamond mine (?), employer - Pittsburg Hood Co., Hazzard, Wash Co., Pa.
Nearest relative - Mrs. Elizabeth Patterson, William Hill, Monongahela, Wash Co., Pa.
Tall, medium build, blue eyes, brown hair

I think it's best to keep trying to narrow down where he was living and when was the latest he was alive.  I tried looking for Bernard or his wife on the 1930 Census, and didn't have any luck.  Maybe another set of eyes will do the trick. 

Sometimes, city directories will give a date of death or tell where people moved to, so you might want to see if you can get a look-up for the Philadelphia city directories for that time frame.  If you check www.raogk.org, there seem to be 2 people in the Philadelphia area doing look-ups in libraries.