Back Everything Up In A Single File?

Greetings,

Our former SQL Server 2000 DBA backed up everything in a single disk
file. By everything I mean, full backup, differential backup and
transaction logs. See below for details of how the backup is currently
set up. When I did 'view contents' of DBBackup, I saw it contained the
mixture of log, full and diff backups of verious dates. She has quit.
Other coworkers said (in a not-sure tone) she was able to restore the
databases from such a single file, although nobody ever saw or knew how
she did recovery. My knowledge about SQL Server, especially regarding
its backup/restore is limited. But I've ever worked with other
databases, e.g. Oracle, MySQL and Postgres. I think log backups, full
backups and differential backups should be completely separated. Also,
in each type of backups, each database should have its own backup file.
Please advise.

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Log backup:

CREATE PROCEDURE sp_lbackup AS
Backup log AGEP To DBBackup
Backup log careerfairs To DBBackup
Backup log CoEdocuments To DBBackup
Backup log committee To DBBackup
Backup log conference To DBBackup
GO

Full backup:

CREATE PROCEDURE dbo.sp_fullbackup AS
Backup database AGEP To DBBackup WITH INIT
Backup database CoEdocuments To DBBackup
Backup database careerfairs To DBBackup
Backup database committee To DBBackup
Backup database conference To DBBackup
GO

Diff backup:

CREATE PROCEDURE sp_diffbackup AS
Backup database AGEP To DBBackup with differential
Backup database careerfairs To DBBackup with differential
Backup database CoEdocuments To DBBackup with differential
Backup database committee To DBBackup with differential
Backup database conference To DBBackup with differential
GO
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Thanks in advance for any help,

Bing